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A New Implicit Scheme for Solving 3-D Shallow Water Flows

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Abstract

Based on the improved ADI method, this article proposes an improved implicit finite difference scheme for solving 3-D shallow water flows. The main objective is to design a numerical relation between the horizontal velocity on each layer and the depth-averaged velocity for employing the improved ADI method. With the free surface elevation and the depth-averaged velocity obtained by using essentially 2-D depth-averaged mode, the velocity profiles can be obtained easily and simultaneously. The wind-induced flows, the open channel flows due to the pressure gradient and the tidal flows in coastal waters are simulated, and the results are consistent well with the analytical solution and the field data, which shows that the present implicit scheme is stable and effective, and the established model is practical. Moreover, when only one vertical layer is specified, the present 3-D numerical model is reducea to the 2-D depth-averaged model.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology Water Resources and Hydraulic Engineering, Ocean College, Hohai University, Nanjing, 210098, China

    Zhuo Zhang

  2. Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing, 210097, China

    Zhi-yao Song & Guo-nian Lv

Authors
  1. Zhuo Zhang
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  2. Zhi-yao Song
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  3. Guo-nian Lv
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Corresponding author

Correspondence to Zhi-yao Song.

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 40730527), the Public Fund Project from Ministry of Water Resources (Grant No.200701026) and the Open Fund of State Key Laboratory of Resource and Environment Information System, Hohai University, (Grant No. 2007491211).

Biography: ZHANG Zhuo (1981-), Male, Ph. D. Candidate

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Zhang, Z., Song, Zy. & Lv, Gn. A New Implicit Scheme for Solving 3-D Shallow Water Flows. J Hydrodyn 21, 790–798 (2009). https://doi.org/10.1016/S1001-6058(08)60214-0

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  • DOI: https://doi.org/10.1016/S1001-6058(08)60214-0

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